On modulus of continuity of differentiation operator on weighted Sobolev classes

TL;DR

This paper studies how smoothly the differentiation operator acts on weighted Sobolev classes of functions with specific monotonicity properties, focusing on the modulus of continuity in this context.

Contribution

It provides new insights into the modulus of continuity for differential operators on weighted Sobolev classes with monotonic majorants, extending existing theoretical frameworks.

Findings

Derived bounds for the modulus of continuity of differentiation operators.

Characterized classes of functions with specific monotonicity properties.

Extended classical results to weighted Sobolev spaces with non-increasing majorants.

Abstract

In this paper we investigate the modulus of continuity of differential operator of order $k$, $k\in\mathbb{N}$, on the classes of functions defined on half-line that have positive non-increasing continuous majorants of functions and their higher derivatives.